ON THE DETERMINANTS OF CONVERGENCE AND DIVERGENCE ...

investigaciones económicas. vol. XXVIII (1), 2004, 89-121

ON THE DETERMINANTS OF CONVERGENCEAND DIVERGENCE PROCESSES IN SPAIN

LEONE LEONIDAUniversità Degli Studi Della Calabria

DANIEL MONTOLIOUniversitat de Barcelona

This paper studies the dynamics of convergence and divergence in Spain overthe period 1965-1995. We analyse the evolution of the per capita income dis-tribution across Spanish provinces and estimate the e ects on this evolutionof factors such as private, human and public capital, and an industrialisationindex. We show that after a period of absolute convergence over the 1960sand early 1970s, the provinces polarised (club convergence) during the 1980s.This polarisation process preceded a period of divergence among clubs, whichbegan to appear during the 1990s. By estimating counterfactual densities, weshow that private capital accumulation and education at graduate level canaccount for a relevant fraction of the actual dispersion and polarisation ofincomes. We also find that public capital has reduced inequalities, especiallyin recent years, through redistribution of incomes rather than by increasingproductivity.

Keywords: convergence, factors of production, industrialisation,non-parametric density estimation.

(JEL C14, O40, O41)

1. Introduction

The regression approach is still the framework of reference for eco-nomists who aim to analyse the empirical determinants of economicgrowth and convergence processes across economies. However, recently,

We thank G. Baiocchi, J. Hutton, G. Ozkan, P. Simmons and all the participantsto the ´ ´ for helpful comments. In particular,we are in debt to S. Bentolila and two anonymous referees; their comments andsuggestions have considerably improved our paper. We want also thank M. Masfor kindly providing the information necessary to construct our measures of humancapital stock. Any remaining errors are ours. Acknowledges financial support of theSpanish Ministerio de Ciencia y Tecnología (CICYT SEC2000-0876).

90 investigaciones económicas, vol xxviii (1), 2004

a completely di erent approach has emerged, focusing on the analy-sis of the entire distribution of per capita income across a sample ofeconomies rather than only on its mean and variance (Quah, 1997).

From the perspective of the debate on growth determinants, this newapproach allows to relax the hypothesis, implicit in a “growth regres-sion” framework, that the growth process is common to all economies.If the latter is not the case, an analysis which examines the overalldistribution of incomes provides us with more information than theanalysis of the conditional mean.

Density estimation has been extensively applied and interesting newstylized facts have been found (Quah, 1997; Paap and van Dijk, 1998;Bianchi, 1999; Lamo, 2000). However, this approach needs some refine-ments especially when applied to the study of growth and convergenceissues (Quah, 1996). We are convinced that its main shortcomings aredue to the necessity of estimating distributions by means of a com-plete non-parametric technique, since it is free from any theoreticalconstraint. This estimation framework is particularly appealing to thestudy of the dynamics of a set of economies with respect to their growthand convergence processes, but such lack of economic structure makesthe econometric results di cult to interpret in the light of economictheory: the strength of the non-parametric technique in uncoveringif a sample of economies grows and converges represents its primaryweakness when the researcher wants to address why one observes gro-wth, convergence or divergence. In fact, it is di cult to assess withina completely non-parametric setup questions like “Are private, humanand public capital stocks sources of economic growth?” or “Do thesevariables promote convergence across economies?”

Thus, the aim of the present study is twofold. First, we study the dyna-mics of the per capita income distribution across the Spanish provincesover the period 1965-1995 using the same methodology as Lamo (2000),i.e. non-parametric techniques. Lamo (2000) focuses on the empiricalestimation of stochastic kernels to estimate the degree of persistencein income disparities across the Spanish provinces. We address this is-sue again because we believe that the time structure of the transitionsshe uses, transitions occurring every year in the distribution, tends tohide interesting features of long run growth processes. We show thatif the time span is allowed to be longer than in Lamo (2000), as forexample in Quah (1997), medium run changes in the composition of“middle class” provinces define the long run processes of growth and

l. leonida, d. montolio: convergence and divergence in spain 91

convergence in Spain, even if the sample displays persistence in incomedisparities in the short run. We show that, after a period of absoluteconvergence over the 1960s and early 1970s, the provinces polarised(club convergence) during the 1980s. This polarisation process prece-ded a period of divergence among clubs which began to appear duringthe 1990s.

Second, we refer to the evolution of the actual distribution rather thanits steady state characteristics in order to define an estimation fra-mework linking economic theory with the non-parametric framework.Using a conditioning scheme directly derived from economic theory,we remove the e ects of some “economic fundamentals” from the evo-lution of the per capita income distribution obtaining “counterfactualdistributions” (Di Nardo, Fortin and Lemieux, 1996). The di erencebetween the actual and the counterfactual distribution is a measure ofthe e ects of the “washed-up” variable on growth dynamics. Our e ortresults in a semi-parametric approach which yields information on thee ects of variables such as private, human and public capital and anindustrialisation index on growth and convergence processes observedin Spain over the last decades. Hence, the resulting framework leads toan empirical analysis that is closer (and with comparable results), toa more traditional “growth regression” with regard to the estimate ofthe steady state only.1 A number of interesting new stylized facts emer-ge from our analysis. We show that private capital accumulation andeducation at the graduate level can explain the growth process of richprovinces and a relevant fraction of the dispersion and polarisation ofincomes, while public capital has reduced income inequalities, especia-lly in recent years, through redistribution of incomes rather than byincreasing productivity. Finally, industrialisation, once estimates arecontrolled for all the other determinants, accounts for only a smallerfraction of such processes.

The paper is organised as follows. Section 2 briefly reviews the theo-retical and empirical debate on growth and convergence, with specialreference to the Spanish literature. Section 3 describes the methodo-

1 It is worth mentioning that the usual practice in the literature we refer to is to useper capita GPD of each single economy normalised by the average per capita GDPacross the sample (see for instance Quah, 1997). For this reason, conclusions onconvergence may be directly drawn from this type of analysis, while conclusions ongrowth may only be indirectly drawn: if a growth determinant causes convergence,it would mean that, for instance, it has a high e ect on poor economies, makingthem to grow faster than richer ones.


logy we employ. Section 4 presents the variables and data used inthe empirical estimations. Section 5 reports our empirical results onconvergence across Spanish provinces. Section 6 presents our resultswith regard to counterfactual densities. Finally, Section 7 sums up ourconclusions.

2. Growth and convergence in Spain

Classical models à la Solow (1956) and their predictions on convergen-ce have been subjected to many kinds of empirical tests and furthertheoretical developments (see for instance, Barro and Sala-i-Martin,1996 or de la Fuente, 1997 for a summary). The empirical evidenceargues against “absolute convergence” if such a hypothesis is testedacross economies with di erent levels of development (Baumol, 1986).This finding led to the development of the “conditional convergencehypothesis” by authors such as Barro and Sala-i-Martin (1991) andMankiw, Romer and Weil (1992), which provides the main theoreticalframework for introducing di erent variables as growth determinants.Conditional convergence provides a framework that captures the exis-tence of di erent steady states when testing for convergence; in otherwords, the idea is to control for structural variables that determinethe steady states towards which the economies are converging. Usingthis framework, growth models have been “augmented” to account forvariables such as human and public capital as growth determinants.

Growth and convergence issues in Spain have been mainly studiedusing such “convergence equations”, and focussing mainly on regionaleconomies. Pioneering works include Raymond and García-Greciano(1994), who investigated growth and convergence at the regional level,and Dolado, González-Páramo and Roldán (1994), who analysed theprovincial case2. Recently, Lamo (2000) has applied a non-parametricframework to the Spanish provinces. She studies long run tendenciesin provincial economies by projecting their realised growth tenden-cies, and by estimating a proxy of the steady state distribution. Sheestimates stochastic kernels on the basis of one-year transitions, andconcludes that persistence of income disparities is the main feature ofthe sample, which is robust to migration processes. Her results hold,

2These studies were followed by other regional studies such as de la Fuente (1994),García-Greciano et al. (1995), Mas et al. (1994, 1995), Cuadrado et al. (1999) orSalas (1999). Using di erent specifications and econometric tools convergence hasbeen a common result in these works.


in our opinion, because she analyses transitions between and + 1only; given the persistence that per capita income usually shows, thisseems a choice that may hide interesting features of long run growthprocesses.

In line with the conditional convergence approach, di erent variableshave been introduced into growth regressions to check whether theyhelp to predict Spanish growth rates. For instance, Gorostiaga (1999)estimates a growth model with human and public capital using pa-nel data with instrumental variables for the Spanish regions over theperiod 1961-1991. The conditional convergence hypothesis of hetero-geneity of steady states is accounted for by means of fixed regionale ects. She finds a convergence rate higher than the usual 2% (18%),and robust to the introduction of human and public capital into the es-timation. Moreover, introducing human capital improves the estimatesof the convergence equation indicating the possibility that this varia-ble plays, on average, an important role in growth and convergenceprocesses in Spain. Results for public capital as a growth determinantare less optimistic.

Recently, de la Fuente (2002) has pointed out the adequacy of estima-ting more disaggregated growth models (i.e. including more potentialgrowth determinants) for a better understanding of observed growthprocesses. Even if the e ects of these growth determinants on growthrates are significant or not in the classical approach, an analysis of theire ects on the per capita income distribution across Spanish provincesis needed, since their average e ect may not hold for all the quantilesof the distribution. For example, the positive e ect that private capitalhas, on average, on growth rates may be the composition of a strongpositive e ect on only some provinces and an e ect close to zero on ot-hers. The analysis of the income distribution would shed light on whichpart of the distribution benefits from capital accumulation. Moreover,the controversial e ects of public capital on growth and convergencefound, among others, by Gorostiaga (1999) or González-Páramo andMartínez (2002) do not mean that public spending has no e ect onthe distribution of incomes: if governments use public spending to re-distribute income, then the positive e ect on poorer economies maybe o set, on average, by taxation of richer areas. This could be thereason why the e ect of public spending on the mean of growth ratesis usually negligible (or even negative); in any case, both e ects should


be highlighted via the analysis of the overall distribution of incomes,as in the present study.

3. Methodology

This section presents both the methodology that we use to study theevolution of the distribution of incomes, and the technique that allowsus to estimate the e ects of a vector of “potential” growth determi-nants on the income distribution. We use a number of tools developedby authors studying the e ects of alternative factors on the income dis-tribution at the household level, and we apply them to the convergenceliterature for what is, as far as we know, the first time.

Let be the relative per capita income of the province at time ,where = 1 and = 0 , and a set of characteristicsthat economic theory suggests influence . Let ( ) be the per capitaincome distribution and ( ) the distribution of characteristic,both taken at time . Our aims are to describe the evolution of the percapita income distribution ( ) through , and to show the e ect of( ) on ( ) across time, holding constant all other 1 growthdeterminants.

3.1. A direct analysis for growth and convergence

Our first step consists in estimating densities, ( ) for all1965 1995 independently. We adopt a completely non-parametricdensity estimation approach; the only assumption we need is that( ) exists and it is su ciently smoothed (Silverman, 1986). Defi-

ne a kernel function as: Z( ) = 1 [1]

Given , a broad class of density estimators may be defined as:

ˆ ( ) =1 X

=1

µ ¶[2]

where is the total number of observations in the sample, and isthe bandwidth (the smoothing parameter); (·) refers to a kernel andis per capita income of the observation of the sample.

Alternative kernel functions may be applied to the sample; each ofthem has di erent advantages and disadvantages (especially in terms of


e ciency and smoothing power). We make use of the Gaussian kernel,that is, the height of the standard normal distribution evaluated at

, given a bandwidth . The choice is due, essentially, to itsproperty of monotonicity of features, peaks and valleys, with respectto changes in the bandwidth magnitude; this property is particularlyuseful when comparing distributions over time (Silverman, 1986).

The bandwidth choice ( ) is the crucial issue in the e ective estima-tion of the density functions. In general, the bigger the bandwidth,the more smoothed the estimated densities; we use the Sheather andJones (1991) smoothing parameter; however, we perform a number ofrobustness exercises, and show that results do not substantially changewith di erent smoothing parameters.

Note that the estimates are performed independently for all ; for thisreason, distributions relative to di erent years have a di erent “op-timal” bandwidth. Unfortunately, it is not possible to compare dis-tributions estimated using di erent smoothing parameters: “when itis desired to compare several density estimates, meaningful compari-son (of densities with comparable “features”) can only be done whenthe same amount of smoothing is done for each curve” (Marron andSchmitz, 1992). Given that the data used have the same scale andthe same cross-section dimension, Marron and Schmitz (1992) suggestthe application of the average amount of optimal smoothing to eachestimate.

3.2. Weighted Kernel density estimation and counterfactual densities

To analyse the e ects of conditioning variables on ( ), fix again,and define the density of as:

( ) =

Z( | ) ( ) [3]

where (·) is the conditional density of , given a set of characteristicsand their joint distribution ( ).

Suppose there exists a qualitative variable , assuming value 1 ifthis characteristic is present and 0 otherwise (for instance, high/lowprivate capital stock, or belonging to a particular cluster in the incomedistribution). We can define the (conditional) density representing the


distribution of the variable in the sub-samples for which the factoris absent and the density where the factor is present as:

( | = 0) =

Z( | = 0) ( = 0) [4]

and,

( | = 1) =

Z( | = 1) ( = 1) [5]

respectively.

To highlight the e ect of the qualitative variable on the whole dis-tribution, we should estimate the distribution that would prevail ifall observations had/did not have the characteristic represented by .Why not compare these distributions with each other as an e ect ofthe presence of ? Densities in [4] and [5] cannot be compared with ea-ch other, nor with density in [3]; it is true that they are constructed byusing the presence of as discriminant; however, the di erence betwe-en these distributions cannot be imputed to only: all the remaining

1 variables must be kept constant.

Johnston and Di Nardo (1997) suggest that we should estimate

( ) =

Z( | = 0) ( ) [6]

which is exactly the distribution that would prevail at time if allprovinces did not possess the factor . The application of Bayes’ law

( ) =( = 0) ( = 0)

( = 0 | )[7]

and substitution of this expression in [6], yields

( ) =

Z( | = 0) ( = 0) [8]

( ) = ( | = 0) [9]

where

=( = 0)

( = 0 | )[10]

Equation [9] proves that, to obtain the counterfactual density ( )in [6], we need a measure of and the density relative to the sub-samples for which = 0. Therefore, three issues must be addressed:


the meaning of parameters , and how to estimate and use them in anon-parametric density estimation approach.

What is ? The answer is closely related to the construction of thesub-sample in [4] and [5], and to the meaning of Bayes’ law in [7].It should be remembered that the densities relative to the two sub-samples cannot be directly compared with each other, nor with thedistribution relative to the overall sample. The reason for this is thatthese sub-samples are di erent in construction, but we cannot be surethat the presence of represents the only di erence among these threesamples.

This can be made clear by rearranging equation [7] as follows:

( )

( | = 0)=

( = 0)

( = 0 | )[11]

The ratio between the two densities in equation [11] is di erent tounity unless is independent from . In a growth framework thiswould hardly be the case: we want to hold all variables constant apartfrom For example, suppose = 0 represents “having a low privatecapital stock”. However, being an “ = 0” observation may meanhaving other di erent features; for instance, it may mean having alow level of human capital. If this is the case, in the “ = 0” sub-sample, there are many observations with low human capital; suchobservations are overrepresented, and observations with a high level ofhuman capital are underrepresented.

For this reason, di erences in per capita income distribution acrosssub-samples are actually due both to and to the di erent distribu-tion of human capital ( ( | = 0)) with respect to the overall sample( ( )). To estimate the e ect of only, we must correct the estimatesfor this second e ect, the intention being to re-weight the sub-samplesby giving more weight to underrepresented and less weight to overre-presented observations.

The estimated has exactly this function: it is a re-weighting vec-tor. Suppose that is present in 50% of the observations: ( =0) = 0.5. Following our example, in the sub-samples constructed from= 0 there are many observations having a low level of human capital:( = 0 | ) is then greater than 0.5 for these observations. Equa-

tion [10] shows assigns them a score smaller than 1. In the same sub-sample, observations with high human capital have ( = 0 | )


smaller than 0.5: assigns to these observations a score greater than1. In short, by applying all densities are made directly comparable,and the di erence would be due to only, not to the other 1variables.

Estimates of , ˆ , may be obtained noting that in equation [10] thenumerator ( ( = 0)) indicates the proportion of observations nothaving the factor ; the denominator ( ( = 0 | )) may be obtai-ned by applying a probit model3, defining the conditional probabilityof having/not having the factor as a function of a vector of the other

1 characteristics. Having ˆ , and applying

ˆ ( ) =1 X

=1

ˆµ ¶

[12]

gives an estimate of [6].

The distance between the actual and the counterfactual densities, ob-tained by re-weighting the sub-sample where = 0 measures theactual e ect of on the income distribution (Di Nardo, Fortin andLemieux, 1996)4. A similar measure would be obtained by re-weightingthe samples for which = 1; in this case, weights would be ˆ = 1 ˆ .

4. Data description

We use as a measure of per capita income Gross Domestic Product(GDP) for the period 1965-1995 across 50 Spanish provinces, exclud-ing Ceuta and Melilla. Data comes from the Fundación Banco BilbaoVizcaya (Fundación BBV, 1999). This institution provides a homoge-neous GDP series from 1955 to 1997 at 1986 constant prices; we use

3Using the full vector of independent variables we estimate a probit of the form:

( ) = (y)

where ( ) stands for the dichotomic variable ( ) for the private capital, yfor the vector of independent variables, and finally, is the probabilistic functionused in the estimations. This procedure is repeated for the other variables used,changing adequately in each case the dependent and independent variables of theprobit estimation.4The reverse e ect of on the factor is controlled by holding constant this variablewhen estimating the probit (i.e. including it in the regressor set). Clearly, we couldshow the e ects of the GDP on the accumulation of each factor; however, this taskis beyond the scope of this paper.


population series, also from the Fundación BBV (1999) for normaliza-tion5.

For our conditioning exercise, we use private capital, human and publiccapital stocks and a measure of sectoral structure. Figure 1 showsthe evolution of these variables across provinces and the period ofexamined. Moreover, table 1 presents some descriptive statistics of thedata.

5The Fundación BBV (1999) data base is on a biannual basis; for our purposesthis characteristic does not a ect the results because we estimate the densities ateach point in time. Moreover, following Quah (1997), we have calculated the ratiobetween the per capita value (in each year and for each province), and the percapita average for Spain. This normalization is very useful in two aspects. Firstly,it is an easy way to abstract from Spain’s total growth and fluctuations. Secondly,since the average for Spain is equal to one, the data assumes the form of dispersionaround the Spanish average, and it is possible to make direct comparisons acrossyears. Therefore, the data is expressed, and labelled in the figures, as relative tothe Spanish average.

FIGURE 1Factors of production


Private capital stock series is measured as the sum of all private ac-tivities (Fundación BBV, 1999). Series are in millions of pesetas at1986 constant prices. The distribution of private capital is bimodalin the initial and final year of our span (panel [a]), indicating pola-rization of economic activities. The group of provinces with a highstock of private capital create a mode around 1.5 in the private ca-pital stock distribution; the remaining provinces are concentrated inthe prominent mode, set around the Spanish average. Private capi-tal levels experienced a period of convergence until 1981; after thisyear, some provinces accumulated more private capital than others.This process created a di erentiated cluster, during the nineties, inthe private capital distribution.

We use two measures of human capital stock. First, we use a weightedmeasure of the total number, in each province, of workers with di erentlevels of education attained. Following Mincer’s work (1974), whichrelates the salary obtained to the level of education and training, wemeasure human capital as:

= [13]

where is the human capital stock, is the average returns on scho-oling, is the overall level of workers in province and is the

TABLE 1Descriptive statistic of main variables. Spain 1965-1995

Average 1965-1979

Variable Min 25% Median Mean 75% Max

GDP 0.5414 0.7007 0.8255 0.8982 1.0450 1.4360Private Capital 0.5155 0.7207 0.8530 0.9137 1.0490 1.5170Human Capital 0.7596 0.8771 0.9800 0.9803 1.0850 1.2990College Education 0.4552 0.5987 0.7785 0.8059 0.9215 2.4270Public Capital 0.6171 0.8299 1.1070 1.2820 1.5640 3.9640Sectoral Structure 0.7657 0.9032 0.9723 0.9776 1.0390 1.2420

Average 1981-1995

GDP 0.5985 0.7442 0.9148 0.9296 1.0800 1.4210Private Capital 0.5514 0.8144 0.9632 0.9782 1.0700 1.7940Human Capital 0.6968 0.8944 0.9961 0.9831 1.0860 1.2610College Education 0.3860 0.5663 0.7779 0.8014 0.9486 2.0960Public Capital 0.7110 0.8697 1.1470 1.2700 1.4930 3.1970Sectoral Structure 0.7650 0.8815 0.9565 0.9638 1.0150 1.2970


average years of schooling of the working population in each province,measured as:

=X

[14]

where represents the level of instruction attained, is the numberof years necessary to obtain the level of education, and is thenumber of workers in province with a level of education .

Data on the number of workers for each level of studies is from theInstitut Valencià d’Investigacions Econòmiques (IVIE). We take fivelevels of education into account; the corresponding numbers of yearsnecessary to obtain the level of education ( ) are: illiteracy (0),primary school (3 5), secondary school (11), university (16), and thehigher degrees of university or college graduates (17). As a measure ofreturns to schooling, , we use the estimate of Alba-Ramírez and San-Segundo (1995), who calculate the Mincerian specification of earningsequation in Spain, obtaining a value of 8.36%, which does not substan-tially di er from the 8.5% estimated for Europe (see Psacharopoulos,1994).

The distribution of this measure of human capital stock was bimodalin 1965 (panel [b] in figure 1), with two di erentiated clusters of pro-vinces (above and below the Spanish average). Over time, those pro-vinces with low human capital concentrated in a more distant clusterthan in 1965. The bimodal shape of 1995 human capital distribution ischaracterized by some provinces moving towards the Spanish average,leaving behind the cluster of provinces endowed with relatively lesshuman capital.

As a second measure of human capital we use the number of wor-kers with college education6. In using this proxy, our aim is to studythe e ect of high levels of education on growth processes. Notice thatthis variable is completely di erently distributed when compared tothe other measure of human capital (panel [c]). Although there was aprocess of homogenization of the distribution across Spanish provin-ces, the distribution presents a long right tail, indicating that a fewprovinces concentrate a high number of workers with college graduatestudies.

6This variable di ers from the variables usually employed to proxy for the humancapital stock. We thank an anonymous referee for this suggestion.


Public capital stock is expressed in millions of pesetas at 1986 constantprices. We define the total public capital stock as the sum of all typesof public capital, which includes two main groups: productive publiccapital (infrastructures in roads, highways, water and sewer systems,urban infrastructures, harbors, railways and airports) and social publiccapital (health and education infrastructures). Its distribution (panel[d]) shows two modes in 1965, with a few provinces endowed withhigh stocks of public capital. In 1995 the provinces are concentratedin a prominent mode; a few provinces create a cluster, set at twicethe Spanish average. From 1965 to 1995 provinces from both tails ofthe distribution tend towards the Spanish average. In general, “poor”provinces are endowed with a higher level of public capital; this con-firms the idea that public capital stock has been used by governmentto develop depressed areas.

Finally, we construct an index capturing the sectoral composition ofeach province. We use the provincial Gross Value Added (GVA) seriesin millions of pesetas at 1986 constant prices, disaggregated into thethree main sectors of the economy: agriculture, forestry and fishing; in-dustry, energy and construction; and services (Fundación BBV, 1999).We use the series of workers in each sector (IVIE). The index is cons-tructed as7:

=+

+[15]

5. The evolution of the per capita income distribution

Figure 2 shows results that summarize the evolution of the per capitaincome distribution across the Spanish provinces. Panel [a] comparesthe density estimates for 1965 and 1995; panel [c] presents their smoot-hed di erences, which help to characterise the processes of convergenceand growth. Panels [b] and [d] show, respectively, an estimate of theevolution of the density between 1965 and 1995 and its contour plot.

7Note that the index pools together the services and industrial sectors. This follo-ws part of the literature across growth and convergence studies (see for instanceDowrick, 1989 and Dowrick and Gemmell, 1991); the idea is that development pro-cesses represent a shift of resources from agricultural to all other sectors.


Finally, panel [e] presents the relative position of each of the provincesin 1965 and 19958.

In 1965 the distribution shows three groups of provinces, clusteredaround 0.7, 1 and 1.5 of the relative per capita income distribution(panel [a] in Figure 2)9. In 1995 the income distribution has less va-

8The contour plot of the bivariate density estimation of the joint distribution fortwo years (panel [e] in figure 2), gives the dynamics between these two particularyears. All observations below the 45-degree line (dashed) correspond to provincesthat lost positions in the income distribution from the year represented in the x -axis with respect to the year in the y-axis. Of course, the argument is the oppositelooking at points above the 45-degree line. For more details on inter and intradistributional dynamics for the Spanish case, see Leonida and Montolio (2001).9For clarity reasons, we have labelled provinces in three main categories: “poor”,“middle class” and “rich” depending on wether their per capita income was below,around or above the Spanish average, respectively.

FIGURE 2Evolution of the relative per capita income distribution


riance; moreover, provinces are clustered into two groups. The smoot-hed di erences plot (panel [c]) shows that those provinces set on bothtails of the distribution have converged to the centre, but creating twodi erent clusters (above and around the Spanish average). Therefore,we observe a process characterized by both absolute and club con-vergence. This may be surprising since absolute and club convergencehave been seen in the empirical literature as competing hypotheses.However, it seems reasonable that in a general process of convergenceinvolving all provincial economies, developed provinces may convergefaster towards one another, forming groups and separating from theothers (club convergence). This does not exclude the possibility thatsuch clusters may converge (absolute convergence) or diverge (absolu-te divergence)10. In contrast to Gardeazábal (1996) and Lamo (2000),we found an overall process of convergence and polarization of inco-me (club convergence) across the Spanish provinces during the period1965-1995.

These results do not change if we perform robust estimations of theper capita income distribution. We re-estimate the densities with a15% deviation from the optimal Sheather-Jones bandwidth used inthe estimates presented in Figure 2. We also calculate averages for ea-ch decade, to remove short run e ects of fluctuations. Results of theseexercises are reported in Figure 3: panels [a] and [b] present the esti-mates of 1965 and 1995 with ±15% of the optimal bandwidth; panel[c] presents the 3D evolution of the income distribution for averagedyears, and panel [d] is the comparison between the density estimatefor the time average 1965-1969 and 1991-1995. Moreover, we performall the density estimates and the robustness exercises using the Cross-Section Least-Squares bandwidth (figures not reported).

More results can be extracted from Figure 2. The convergence patternfound was not, and is not uniform; periods of convergence may ha-ve been followed by periods of divergence. The methodology employedallows us to determine endogenously the relevant periods and not to ta-ke them as given, as in other studies. Panels [b] and [d] in Figure 2 showthat the overall period may be decomposed into four sub-periods in

10Leonida (2002) shows that testing for convergence using absolute and club con-vergence as competing hypotheses is intuitively appealing, but may be misleading:evidence in favour of the latter may or may not reject the former.


which the dynamical path of the provinces is substantially di erent11.From 1965 to 1977 the provinces experienced a period of convergence:per capita income of those provinces grouped around 0.7 of the inco-me distribution increased to 0.8, approaching the middle class, whilerich provinces lost relative positions, also approaching the middle class(from 1.5 to 1.4 in the per capita income distribution). This result isin contrast with the evidence presented by Dolado, González-Páramoand Roldán (1994), who found for a similar period (1994-1977) noevidence of convergence, but in line with Goerlich et al. (2001), whopointed to convergence in labour productivity across provinces as apossible factor explaining this process.

11 In figure 2 panel [d], the countour plot of the evolution of the income density, thevertical axis indicates the 16 years available in the biannual data base (from 1965to 1995).

FIGURE 3Robustness Exercises


A second period runs from 1977 to 1983. Over these years there was aprocess of polarization of income: the convergence process observed inthe previous period came to an end. In 1983 there were two clustersof provinces, mainly because the rich provinces continued to lose posi-tions, approaching the middle class. Particularly significant is the lossof positions of those provinces (mainly in the Basque Country) thatsu ered the decline of the industrial sector.

In a third period, running from 1983 to 1993, some of the middle classprovinces shifted to the poor group and some grew enough to approa-ch the richest group of provinces that, in turn, were concentrating ata lower level of the relative per capita income distribution. This pro-cess leads to a “vanishing middle class”, and therefore, a polarizationprocess.

Over the last years analysed (1993-1995) provinces continued to clusterin two di erentiated groups, and began to diverge. In 1995 the incomedistribution shows a second mode, emerging at about 1.2 of incomedistribution. Moreover, a divergence process can be also detected overthe nineties: the richest provinces not only create a significant mo-de, but also separate from the other group of provinces (the distancebetween modes was greater in 1995 than in 1993).

We complete and enrich our analysis by showing which provinces havechanged cluster in the income distribution through time. Panel [e] inFigure 2 shows the relative position of each of the provinces in 1965and 1995. These results confirm our previous findings. The rich pro-vinces in 1965, which had an income per capita higher than 60% of theSpanish average, have lost relative positions; however, in 1995 they stillcompose the rich cluster showing persistence in relative positions andincome disparities (Álava, Baleares, Barcelona, Girona, and Madrid).Especially significant is the evolution of Guipúzcoa and Vizcaya: fromthe highest part of the distribution in 1965 to lower positions muchcloser to the Spanish average (but still forming part of the rich clusterin 1995). Moreover, in 1995 these provinces are matched by eight otherprovinces; five from the middle-income class in 1965 (Lleida, Navarra,La Rioja, Tarragona and Zaragoza), and only three from the poorcluster (Burgos, Castellón and Guadalajara): all of them forming theseparated and diverging cluster observed in recent years.

The provinces composing the middle-income class in 1965 split alsobecause four of these provinces moved to the poorer group (Alicante,


Oviedo, Santander and Sevilla). The poor provinces, in general, gainedpositions in the income distribution (except Cádiz); however, not allof them grew enough to change cluster. Five provinces switched fromthe lowest part of the poor cluster to the upper part of the same group(Ávila, Cáceres, Soria, Teruel and Toledo).

Finally, it is worth mentioning that we do not estimate the ergodicdistribution from the realised random fields. This is for two reasons.First, we prefer to estimate the e ects of di erent variables on theevolution of the actual distribution (see next section). Second, thisexercise has been performed by Lamo (2000), and there is no reasonto expect any di erent characterization of the steady state given thetime structure of the transitions she uses. However, losing 6% in therelative per capita income distribution took the richest provinces morethan 10 years; the process that saw poor provinces change cluster last20 years: clearly, interesting long-run changes occurred in the Spanishincome distribution. However, given the persistence that per capitaGDP series usually shows, results from a transitional analysis betweenand +1 may be interpreted as economies being in their steady state(Gardeazábal, 1996, and Lamo, 2000). We believe that the steady statepositions of economies should be characterized in terms of economictheory, rather than by means of a purely empirical approach: as Quah(1996) has pointed out, it is necessary to provide explicit economicmodels to support the recent empirical evidence based on the statisticalquantification of changes in the income distribution.

6. The e ects of growth determinants on the per capita

income distribution

In this section we present the counterfactual results (see Figures 4 to8)12. Each figure contains four panels. We report the actual distribu-tion and its re-weighted counterpart for 1995 (panels [a]) and 1965(panels [b]) to test the hypothesis that the e ect of each of the gro-wth determinants on the distribution can change over time. Panels [c]and [d] show the di erence between each actual and counterfactualdistribution.

12We have only reported the counterfactual densities for the case when = 0because the counterfactual densities for = 1 are a mirror image.


6.1. Does private capital accumulation represent the main source ofgrowth?

In answering this question, first we focus on the e ects of private capi-tal on the income distribution. Private capital accumulation is sugges-ted to be the main determinant of growth, according to both neoclas-sical frameworks of growth (Solow, 1956 or Mankiw, Romer and Weil,1992) and endogenous growth theories (Romer, 1986). As we noted,the analysis of the distribution of private capital stock suggests thatthere exist some structural di erences across provinces with respectto their ability to accumulate private capital. Now we study what thedistribution of incomes would look like if the e ect of this ability wereremoved.

To answer this question, we attach 1 to observations having a highlevel of private capital stock and 0 to all others, and estimate the

FIGURE 4Private capital


probability (using a probit model) of being endowed with high privatecapital as a function of the full vector of independent variables13. Thisprocedure results in the vector of weights ˆ , see equation [10]. Theweights are used to answer the question of interest, which is reportedin Figure 4.

Our exercise suggests, as expected, that the accumulation of privatecapital plays a crucial role in growth and convergence processes. Theestimated counterfactual densities have less variance, and the multi-ple regime of the actual per capita income distribution vanishes: theprovinces would be concentrated in a single cluster, settled below theSpanish average14. This e ect is greater for the rich provinces. Thesmoothed di erence for 1995 shows that these economies would lo-se positions, moving to the lower part of the income distribution. In1965, the counterfactual distribution is characterized by the middleclass and rich provinces concentrating in the lower part of the incomedistribution; however the division into two groups is still in evidence.Therefore, private capital accumulation explains an important frac-tion of the processes of growth of developed economies in Spain. Theability to accumulate private capital enabled a fraction of provincesto grow and to separate from the rest of the observations. For mostof the period private capital has the e ect just described. In someyears, it causes polarization of income into two groups (figures not re-ported). This second e ect is evident especially over the middle 1980s,when the private capital stock distribution is unimodal, indicating thatwhen this variable is equally distributed, the rich provinces still crea-te a separated cluster, possibly because of the e ects of other growthdeterminants.

6.2. Does human capital substitute for private capital in growth pro-cesses?

There is a vast literature arguing that human capital can induce gro-wth. Human capital has been introduced into theoretical models either

13 “High” and “low” levels have been decided on the shape of the per capita privatestock distribution itself. In this context, non-parametric density estimates are used,as suggested by Silverman (1986), as discriminant analysis. The same procedure isused for the other variables.14The opposite counterfactual (not reported) also shows convergence but at a higherlevel of the relative per capita income distribution.


as a vehicle of endogenous growth (Lucas, 1988) or directly into neo-classical production functions as a productive input within a broaddefinition of capital (Mankiw, Romer and Weil, 1992).

The question that interests us here is: “What distribution of incomeswould prevail if the distribution of the human capital stock were equa-lized across provinces”? Our results are reported in Figure 5.

The e ects on growth of the first human capital variable used arepositive, especially in the initial years of our database. However, itse ects on the per capita income distribution are smaller than the e ectsof private capital stock.

Human capital has a greater e ect in those years when the Spanishprovinces still did not have a highly developed educational system. In1965, for example, education was not as di use as it is today; skilled

FIGURE 5Human capital (Weighted Measure)


workers were concentrated in the rich provinces, making big di erencesin terms of production. In recent years, the counterfactual distributionshows the same characteristics of the actual distribution but even morepronounced: polarization of income in two di erentiated clusters. Thisindicates that the rich provinces may be benefitting from other growthdeterminants. In short, we believe that the change in the e ects overtime, bigger over the sixties and seventies and smaller in more recentyears, can be explained by a generalization of the level of educationamong the Spanish working population15.

As a confirmation of this analysis, we obtain di erent results if “collegeeducation” is used as a proxy of human capital (Figure 6).

15de la Fuente (2002) reaches similar conclusions regarding the empirical e ect ofhuman capital on growth.

FIGURE 6Human capital (College Education)


In 1995 the distribution would change from a bimodal (actual) to aunimodal shape (counterfactual). This indicates that the polarizationfound in the 1995 income distribution is partially caused by the une-qual distribution of college graduates across provinces.

Instead, in 1965 the counterfactual density shows an income distri-bution with less variance but still with two di erentiated clusters. In1965 the number of graduates was not large enough to make the distri-bution completely unimodal, and the rich provinces, although havingthe same distribution of graduates as those provinces with less gra-duates, would still create a di erentiated cluster. We can observe thatin recent years, the e ect of this variable is to create a unimodal dis-tribution. Therefore, it seems that the e ect of workers with graduatestudies explains part of the polarisation of income across the Spanishprovinces in recent years.

Summarizing, human capital stock has been an important variablein the growth and convergence processes observed across the Spanishprovinces. During the sixties and seventies having an educated workingpopulation was an important growth determinant. The generalizationof the educational system in Spain implied that in recent years thisrole has been played by workers with high levels of education.

6.3. Does government spending stimulate growth and convergence?

Now we analyse one of the main puzzles in the empirical growth litera-ture: the e ect of public capital. In seminal works by authors such asAschauer (1989) or Munnell (1990) public capital, under the control ofgovernments, has been reported to have e ects on the productivity ofthe economy, and hence, on growth rates. However, these results arecontroversial since in the growth regression framework its estimatedparameters are not robust to di erent estimation techniques. Figure 7presents the results from our conditioning exercise for public capital.

In 1965 public capital has a negligible e ect on the per capita incomedistribution; in recent years, however, public capital seems to havean e ect on the per capita income distribution across the Spanishprovinces.

These results can be interpreted as the consequence of the expansionof the public sector over time. In the initial years of our databasepublic intervention in the form of public capital was not as di use as


is today, and therefore its e ect could not be other than negligible.In recent years, democratic governments have implemented a seriesof public policies leading to the construction of the Spanish welfarestate: investment in public capital has increased and raised Spanishstandards to European level.

The di erence between the actual and the counterfactual estimatedincome distributions for recent years can be interpreted as public ca-pital having a positive impact on convergence but a detrimental e ecton growth. The counterfactual distribution in 1995 is more unequal(two more distant clusters) than the actual distribution: the rich pro-vinces would be richer if public capital was equally distributed acrossprovinces. Interestingly, even the poor provinces would be, on average,richer than they are today. Therefore, if public capital were uniformlydistributed across provinces (after controlling for the other variables),

FIGURE 7Public capital


this would induce the rich provinces to separate more from the poorprovinces, obtaining a more unequal distribution of per capita income.

We interpret these results in the light of two e ects: redistributionand growth e ects. The public sector is less e ective than the privatesector in producing goods and services; therefore, shifting resourcesfrom the private to the public sector tends to reduce the growth pro-cess. However, because public sector redistributes income from rich topoor provinces (creating an unequal distribution of public capital, seepanel [d] in Figure 1) the actual distribution is less unequal than thecounterfactual one. In this sense, public capital promotes convergence(redistributing incomes) but has a negative e ect on growth especiallyacross the rich provinces (possibly through taxation). It is importantto note that even if this seems to be a small but positive e ect of pu-blic capital on convergence, it is not strong enough to create an equaldistribution of income.

These two opposite e ects of public capital (equity versus e ciency)could be the reason why the estimated average e ect of public capital,measured for instance by means of OLS or panel data techniques, mayresult to be negligible or even negative.

6.4. Does industrialisation matter?

If private, human and public capital have been widely introduced intotheoretical models as growth determinants, it is more di cult to esta-blish the e ects of changes in the sectoral structure on growth. Someempirical studies for the Spanish case have used di erent measures ofsectoral structure to investigate its e ects on growth and convergencedynamics (for instance, Raymond and García-Greciano, 1994, Serrano,1999 or de la Fuente and Freire, 2000).

We use a common index of industrialisation to show the e ects on theincome distribution of a shift of resources from agriculture to othersectors of the economy. Figure 8 presents the estimated counterfactualdensities, showing the distribution of incomes that would prevail if allthe provinces had had the same sectoral structure as those provinceswith an economy more dedicated to the agricultural sector.

In 1965 the estimated counterfactual e ect is very small, possibly be-cause over these years the economic structure in Spain was concentra-ted in agricultural activities. In recent years, the sectoral structure has


shifted towards industry and services; therefore, in 1995 the counter-factual estimate presents a more uniform distribution, even though arich cluster in the highest part of the per capita income distributionstill exists.

A general, and partially surprising, result is that industrialisation haslittle e ect on the income distribution. However, we measure indus-trialisation as the shift of resources from the agricultural sector tothe other sectors, holding constant all other variables among which,for example, private capital accumulation is included. Clearly, indus-trialisation drives not only private but also human and public capitalaccumulation (changing the structure of the economy), and thereforewe should first estimate the e ects of industrialisation on capital accu-mulation, and subsequently the e ects of this induced accumulation ofcapital on growth. In other words, we think that the important estima-ted e ect of capital accumulation on growth depends on industrialisa-

FIGURE 8Industrialization


tion; however, it is di cult to decompose these e ects with adequateprecision.

7. Conclusions

This study has enabled us to reach a number of interesting conclusionsthat we believe can shed some light on the growth and convergencedebate in Spain.

First, the use of recent data allows us to conclude that, within anoverall process of convergence, the Spanish provinces have alternatedperiods of convergence and periods of polarization of income and di-vergence. In recent years, club convergence seems to have combinedwith an incipient period of divergence.

During the 1960s, the poor provinces converged towards the Spanishaverage income. At the same time, the rich provinces lost positionsin the per capita income distribution. This finding completes previousstudies claiming absolute convergence: the convergence process obser-ved during the sixties was mainly caused by the rich provinces losingpositions together with the middle class and poor provinces convergingtowards one another. However, over the 1970s, the convergence processhalted: some provinces from the middle class grew and caught up withsome rich provinces while the latter continued to lose positions (crea-ting together a new cluster in the income distribution). Over the 1980s,this middle class vanished (polarisation of income). Some of these pro-vinces lost positions in the per capita income distribution and joinedthe poor provinces; the remaining grew enough to approach the richprovinces. Subsequently, over the 1990s the main group of provincesdid not change their relative position; some of the provinces from themiddle class caught up with the richest ones, creating a new clusterat 1.2 of the income distribution. This implies not only a process ofpolarization of income into two groups, but also an initial process ofdivergence: the two modes begin to separate.

Second, the methodology employed allows us to individuate with pre-cision the evolution of each province within the income distribution.The rich provinces lost many positions in the per capita income dis-tribution, this evolution being specially accentuated for provinces inthe Basque Country (especially Guipúzcoa and Vizcaya). On the otherhand, the poor provinces remained in the poor part of the distribution,except for Guadalajara, which grew enough to move from the poor part


of the income distribution in 1965 to the rich cluster in 1995. Interes-tingly, the movements of provinces with per capita income around theSpanish average (“middle class”) determined many of the convergenceand polarization processes observed in Spain.

Third, analysing the reasons why some provinces have grown morethan others can help policy makers to formulate adequate policies toaddress the issue of income disparities across provinces. Therefore, ouranalysis aimed to discover which factors led to the actual evolution ofthe per capita income distribution, an evolution clearly linked to thechanges over time in the classical factors of production.

In general, the regression framework normally used to estimate theaverage growth e ects of “potential” growth determinants such as pri-vate capital results in estimated parameters that are a weighted sumof the e ect of this variable on the poor provinces (which e ect may beexpected to be negligible) and on the rich provinces (which e ect maybe expected to be strongly positive). The econometric framework wedefine demonstrates that, private capital being mainly concentratedin the rich provinces, its distribution can explain a substantial part ofthe actual di erence between “poor” and “rich” provinces in Spain. Itseems therefore that is the ability to accumulate private capital thatpermits provinces to grow, and therefore, separate from those thathave less private capital.

Human capital stock also has an e ect on the actual income distribu-tion. Education at a graduate level can account for, in recent years,part of the polarisation process observed across the Spanish provin-ces, while in the initial years of our database it seems that it wasthe weighted measure of human capital that played a more importantrole in growth and convergence processes in Spain. This can be explai-ned by the low level of general education in Spain during the sixtiesand seventies, and the posterior development and generalization of theeducational system during the eighties and nineties.

Public intervention has been directed to develop poorer provinces.However, the relationship between per capita income and public po-licies is much less obvious. On the one hand, intervention by publiccapital allows poor provinces to improve their standard of living (viaredistribution of incomes). On the other hand, it seems to reduce thegrowth rate of rich provinces (via taxation). Both e ects combined co-uld be the reason why this variable has been one of the main puzzles


in the empirical literature on growth. Finally, the sectoral structure ofprovinces seems to have a less important e ect on the distribution ofincome.

Of course, our exercise does not explain the total variability and pola-risation of incomes; both because we did not concentrate on variablessuch as financial development, and because a relevant part of inco-me variability is explained by historical events, which a ect both theevolution of the per capita income distribution and the evolution ofgrowth determinants.


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Resumen

Recepción del original, marzo de 2001Versión final, septiembre de 2003

Este trabajo estudia las dinámicas de convergencia y divergencia en Españapara el periodo 1965-1995. Se analiza la evolución de la distribución de larenta per cápita para las provincias españolas y se estiman los efectos en di-cha evolución de factores como el capital privado, humano y público ademásde un índice de industrialización. Se muestra como después de un periodode convergencia absoluta durante las décadas de los sesenta y setenta, lasprovincias se polarizaron (club convergence) durante los ochenta. Dicha pola-rización precedió un periodo de divergencia entre clubes que empezó durantelos primeros años de la década de los noventa. La estimación de densidadescontrafactuales muestra que tanto el capital privado como el número de tra-bajadores con estudios superiores explican una fracción relevante de la actualdispersión de la renta. Además, el capital público ha reducido desigualdades,especialmente durante los último años, a través de la redistribución de la rentamás que a través de incremetar la productividad de los factores.

Palabras clave: Convergencia, factores de producción, industrialización, esti-maciones no paramétricas.

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